In a conventional method to reduce carbon monoxide (hereinafter also referred to as CO) in a reformed gas resulting from steam reforming of a material including an organic compound containing at least carbon and hydrogen, a water-shift reaction (hereinafter referred to as a “shift reaction”) using steam and CO is promoted. To be specific, a shift reaction of an air-fuel mixture containing the reformed gas and the steam is typically promoted under a shift reaction temperature condition, using a noble metal catalyst such as platinum, ruthenium, or rhodium, a Cu—Zn catalyst, or a Fe—Cr catalyst. The shift reaction temperature condition of the shift reaction is approximately 100° C. to 250° C. The catalytic activity of the catalyst degrades depending on an environment or with time. Especially, at low temperatures, the catalytic activity significantly degrades. So, a hydrogen generator capable of maintaining the catalytic activity has been proposed. To be specific, the hydrogen generator operates so as to increase a flow rate of water, decrease a flow rate of the reformed gas, or increase a temperature of the catalyst when the catalytic activity has degraded (see, for example, patent document 1). In order to determine whether or not the catalytic activity has degraded, there has been proposed a technique using a CO sensor (see patent document 1), or a determination device (see patent document 2) that simply makes determination by utilizing a temperature change at a predetermined portion of the hydrogen generator has been proposed.    Patent document 1: Domestic re-publication of PCT international publication for patent application No. 02/026620    Patent document 2: Japanese Laid-Open Patent Application Publication No. 2003-217636